Abstract

I begin with some general remarks concerning the co-evolution of representational forms and mathematical meanings. I then discuss the changed roles of mathematics and novel representations that emerge from the ubiquity of computational models, and briefly consider the implications for learning mathematics. I contend that a central component of knowledge required in modern societies involves the development of a meta-epistemological stance – i.e. developing a sense of mechanism for the models that underpin social and professional discourses. I illustrate this point in relation to recent research in which I am investigating the mathematical epistemology of engineering practice. Finally, I map out one implication for the design of future mathematical learning environments with reference to some data from the "Playground Project".

Item Type:

Article

Additional Information:

This paper originated as an invited keynote address to the 52nd annual conference of the Commission Internationale pour l’Enseignement et l’Amelioration de Mathématiques. (CIEAEM) Italy. 2001. Proposes a new epistemology for mathematical knowledge that is more learnable in the light of its expression with digital technologies. The paper discusses the co-evolution of representational forms and mathematical meanings, before considering the changed roles of mathematics and novel representations that emerge from the ubiquity of computational models. It then considers the implications for learning mathematics. A key contention is that a central component of knowledge required in modern societies involves the development of a meta-epistemological stance – i.e. developing a sense of mechanism for the models that underpin social and professional discourses. I illustrate this point in relation to recent research in which I am investigating the mathematical epistemology of engineering practice. Finally, I map out one implication for the design of future mathematical learning environments with reference to some data from the "Playground Project", a major EU-funded project directed by the author. The original publication is available at www.springerlink.com